Quadratic Performance Task

Objective

SWBAT translate from among verbal, numeric, algebraic and graphical representations of quadratic functions.

Big Idea

Flexibility with quadratic functions is put to the test in this puzzle-like quadratic performance task. Various starting points are provided and the goal is to represent each function in all ways we have studied.

Solve quadratic equations by inspection (e.g., for x<sup>2</sup> = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a Â± bi for real numbers a and b.

Warm-Up

20 minutes

As a warm-up, I present students with the x-intercepts (x=3 and x=-1) and y-intercept (y=6) of a quadratic expression and ask them to use the template Warm-Up Quadratic Functions to practice translating the quadratic into its other algebraic forms, graphing, and reporting interesting features of the graph. This warm-up will be challenging for some students because they will be unsure of how to find the value of "a," the coefficient of the squared term. If they are struggling, I remind them that the y-intercept tells them the coordinates of one point on the curve. I make a second copy of this template on the back of the page so that students who complete the exercise quickly can be given a second, more challenging quadratic function to work with. I find that students generally enjoy the puzzle-like aspect of this activity [MP7].

As students complete the warm-up, I check homework with the homework rubric. If there are questions on the homework I will spend a few minutes answering them before we continue our discussion of solving quadratic equations. As always, I try to maximize persistence in homework problems by providing answers on Edmodo and asking students to check their answers before they arrive in class [MP1].

Warm-Up Quadratic Functions

Edmodo - staying connected after class

Explore and Extend

In the Quadratic Performance Task, each student is given an 11" by 17" piece of paper with a preprinted 7X7 table. Each row contains various starting points for defining a quadratic function and the student's goal is to provide all missing information about that function (standard form, vertex form, intercepts, graph, etc) [MP6].

The idea of this task is to give students the opportunity to persist in a challenging task [MP1] and put everything they have learned about quadratic functions together in one activity [MP2, MP7, MP8].

I ask students to complete this activity independently, although I do not mind if they work side-by-side with another student and check in from time-to time. I do not limit graphing calculator use on this activity but I do ask that they make a sound algebraic argument when translating from one form to the other [MP3]. I discuss my expectations for this type of argument in the reflection Sound Algebraic Arguments.

This activity, although very challenging for students, tends to be very popular and a source of pride for students who complete it. This will take at least an hour for most students to complete.